CAIE P3 2021 March — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionMarch
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using subtraction law
DifficultyModerate -0.3 This is a straightforward logarithm equation requiring application of standard log laws (power rule and subtraction rule) to simplify the right side to ln(x³/3), then equating arguments to get x³ - 3 = x³/3, leading to a simple linear equation. Slightly easier than average due to the algebraic simplification being routine, though students must recognize the correct approach.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

Solve the equation \(\ln(x^3 - 3) = 3 \ln x - \ln 3\). Give your answer correct to 3 significant figures. [3]

Question 1:
AnswerMarks Guidance
1Use law of the logarithm of a product or power M1
( )
AnswerMarks
Obtain a correct equation free of logarithms, e.g. 3 x3 −3 = x3A1
Obtain x = 1.65A1
3
AnswerMarks Guidance
QuestionAnswer Marks
Question 1:
1 | Use law of the logarithm of a product or power | M1
( )
Obtain a correct equation free of logarithms, e.g. 3 x3 −3 = x3 | A1
Obtain x = 1.65 | A1
3
Question | Answer | Marks | Guidance
Solve the equation $\ln(x^3 - 3) = 3 \ln x - \ln 3$. Give your answer correct to 3 significant figures. [3]

\hfill \mbox{\textit{CAIE P3 2021 Q1 [3]}}